英文标题：
《Utility maximization problem under transaction costs: optimal dual
processes and stability》
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作者：
Lingqi Gu and Yiqing Lin and Junjian Yang
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最新提交年份：
2017
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英文摘要：
This paper discusses the num\\\'eraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe the stability of the primal and dual value functions as well as the convergence of the primal and dual optimizers when perturbations occur on the utility function and on the physical probability. We then study the properties of the optimal dual process (ODP), that is, a process from the dual domain that induces the optimality of the dual problem. When the market is driven by a continuous process, we construct the ODP for the problem in the limiting market by a sequence of ODPs corresponding to the problems with small misspecificated parameters. Moreover, we prove that this limiting ODP defines a shadow price.
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中文摘要：
本文讨论了具有比例交易成本的市场中基于numeraire的效用最大化问题。特别是，投资者需要在交割时清算其所有股票头寸。我们首先观察了效用函数和物理概率发生扰动时，原值函数和对偶值函数的稳定性以及原优化器和对偶优化器的收敛性。然后，我们研究了最优对偶过程（ODP）的性质，即从对偶域导出对偶问题最优性的过程。当市场由一个连续过程驱动时，我们通过一系列ODP来构造极限市场中问题的ODP，这些ODP对应于具有小的错误指定参数的问题。此外，我们证明了这种极限ODP定义了影子价格。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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